On Potential as a Loss Function

1.1

I probably spend too much time thinking about potential. What is the highest a person can achieve if they make the correct choice at every opportunity? In a deterministic world, maximum potential would be the argmax over all “timelines” of a person’s success. Naturally, this brings us to the question of quantifying success, but I’m going to take the lazy approach and declare that out of scope. This essay is essentially a pitch for the idea of percentage of potential reached as a useful metric for life. I’ll explain how I precisely define this metric and why I find it useful. I hope that you might find something useful to apply to your own life in it.

1.2

This framework is not interested in defining success. Frankly, it doesn’t need to be, at least not to define itself. The onus is on the user to define and quantify success for themself. So, for the purposes of this exercise, we can suppose that there is a “success function” that can numerically define how successful a person is. This in theory would be specific to each person, as success means different things to different people. In the introduction, I framed potential in a deterministic world. However, that’s probably not reasonable. This is because, in a deterministic world, there is probably a chain of inputs that can accomplish pretty much anything for any person, much like a tool assisted speedrun (TAS) manipulating the RNG of a video game. Therefore, if the maximum potential of every person is uncapped, the metric loses any meaning, and we may as well go back to using absolute success as a metric.

1.3

So, I’m going to impose a couple of (hopefully) reasonable assumptions and restrictions in defining this metric. First, the world is assumed to be stochastic, or, at least, the world as a system exhibits deterministic chaos. Therefore, I modify our definition of maximum potential to take the expectation over all events. One more adjustment I’d like to make is taking an action given available information. Potential is, in large part, impacted by the information one has access to at any given time. E.g., the average person in 1950 has access to far less information than someone now, thanks to the internet. Therefore, their potential is likely impacted. It’s worth noting that this change incentivizes decisions that yield more information, since, as one acquires more information, the best decision one can make, given the information available, gets better.

1.4

So, we now define maximum potential as the argmax over all possible decision chains (given available information) of expected success. The metric we are interested in is the percentage reached of that potential at the end of a timeline. We can call this percentage of maximum potential reached (PMPR).

1.5

I recognize that, at the beginning of this essay, I pitched this metric as a way to determine success over a lifetime. However, PMPR is actually much more usable on a micro scale. As a chain of decisions gets longer, noise in the system ought to increase exponentially. Therefore, it becomes harder to objectively measure the quality of a decision. Therefore, it is better to use this in a more limited context, like a conversation or a project.

2.1

So what makes PMPR a useful metric? Reflection on one’s actions is necessary to improve one’s decision-making processes, but doing so objectively is quite difficult. I often find myself facing two problems during this process: skewed comparison to others and focus on external factors. PMPR helps to mitigate both of these.

2.2

Reflection often leads to comparison with others, which is fine and even necessary to see where one stands. However, comparison is hard to do objectively, since others’ situations often give them certain advantages or disadvantages. It is incredibly easy to end up focusing on these aspects of someone’s performance, rather than their decision making - the only metric that there is any sense in comparing, as it is the only one we can actually improve. Rather, all other metrics are a byproduct of decision making. If decision making improves, the other metrics improve. By framing reflection through the lense of making the best decisions with the information available, one is able to compare one’s decision making to that of others while eliminating noise.

2.3

Similarly, it is easy to focus on external factors when reflecting on one’s performance. In rowing, novices often blame the weather for a bad race. Yet, the reality is, everyone rowed in those conditions. The winner won because their preparation allowed them to win, regardless of conditions. Whether they were at a higher level technically or were simply fit enough that it didn’t matter, their preparation (i.e. their decision making in the days leading up to the race) was simply better than the other racers. By looking at one’s performance in comparison to their maximum potential performance, one focuses on the decisions - the controllable. Tuning out the uncontrollable factors - but to perhaps factor them into one’s decision making next time - and focusing on what one can control is much more valuable - and less emotionally taxing - than the alternative.

3.1

If there is an objectively correct way to utilize PMPR in life, I am yet to find it. Self reflection is inherently personal, and therefore reflecting on the reflection process itself is doubly so. So I leave deciding on how to use these ideas up to you. I wish you luck!

3.2

This is the first long form writing I’ve produced in several years and the first that has fully engaged me in longer. I fear any writing style I may have had has been crushed by years of neglect and access to LLMs. Now it feels somehow both pretentious and reductivist. I’m hoping to find my voice again and perhaps eventually find some ideas worth writing about. Until then, I hope you’ll bear with me.